To do well in the examination. he --- take careful preparations.

The correct word to complete the sentence is:

"needs"

So the complete sentence is:

"To do well in the examination, he needs to take careful preparations."

Explanation:

• "Needs" is the correct form of the verb to agree with the singular subject "he" and to indicate necessity.
• "Need" would be used if the subject were plural or if the sentence were in a different form.
• "Needy" means requiring help or support, which doesn't fit in this context.
• "Needless" means not necessary, which contradicts the requirement for careful preparation.